Semantic Unification A sheaf theoretic approach to natural language

Language is contextual and sheaf theory provides a high level mathematical framework to model contextuality. We show how sheaf theory can model the contextual nature of natural language and how gluing can be used to provide a global semantics for a discourse by putting together the local logical semantics of each sentence within the discourse. We introduce a presheaf structure corresponding to a basic form of Discourse Representation Structures. Within this setting, we formulate a notion of semantic unification --- gluing meanings of parts of a discourse into a coherent whole --- as a form of sheaf-theoretic gluing. We illustrate this idea with a number of examples where it can used to represent resolutions of anaphoric references. We also discuss multivalued gluing, described using a distributions functor, which can be used to represent situations where multiple gluings are possible, and where we may need to rank them using quantitative measures. Dedicated to Jim Lambek on the occasion of his 90th birthday.Comment: 12 page

Parameterized monads in linguistics

A thesis submitted in partial fulfilment of the requirements of the University of Wolverhampton for the degree of Doctor of Philosophy.This dissertation follows the formal semantics approach to linguistics. It applies recent developments in computing theories to study theoretical linguistics in the area of the interaction between semantics and pragmatics and analyzes several natural language phenomena by parsing them in these theories. Specifically, this dissertation uses parameterized monads, a particular theoretical framework in category theory, as a dynamic semantic framework to reinterpret the compositional Discourse Representation Theory(cDRT), and to provide an analysis of donkey anaphora. Parameterized monads are also used in this dissertation to interpret information states as lists of presuppositions, and as dot types. Alternative interpretations for demonstratives and imperatives are produced, and the conventional implicature phenomenon in linguistics substantiated, using the framework. Interpreting donkey anaphora shows that parameterized monads is able to handle the sentential dependency. Therefore, this framework shows an expressive power equal to that of related frameworks such as the typed logical grammar and the dynamic predicate logic. Interpreting imperatives via parameterized monads also provides a compositional dynamic semantic analysis which is one of the main approaches to analysing imperatives

Meaning versus Grammar

This volume investigates the complicated relationship between grammar, computation, and meaning in natural languages. It details conditions under which meaning-driven processing of natural language is feasible, discusses an operational and accessible implementation of the grammatical cycle for Dutch, and offers analyses of a number of further conjectures about constituency and entailment in natural language

Mathematical linguistics

but in fact this is still an early draft, version 0.56, August 1 2001. Please d

A Process Algebraic Approach to Computational Linguistics

Institute for Communicating and Collaborative SystemsThe thesis presents a way to apply process algebra to computational linguistics. We are interested in how contexts can affect or contribute to language understanding and model the phenomena as a system of communicating processes to study the interaction between them in detail. For this purpose, we turn to the pie-calculus and investigate how communicating processes may be defined. While investigating the computational grounds of communication and concurrency,we devise a graphical representation for processes to capture the structure of interaction between them. Then, we develop a logic, combinatory intuitionistic linear logic with equality relation, to specify communicating processes logically. The development enables us to study Situation Semantics with process algebra. We construct semantic objects employed in Situation Semantics in the pi-calculus and then represent them in the logic. Through the construction,we also relate Situation Semantics with the research on the information flow, Channel Theory, by conceiving of linear logic as a theory of the information flow. To show how sentences can be parsed as the result of interactions between processes, we present a concurrent chart parser encoded in the pi-calculus. We also explain how a semantic representation can be generated as a process by the parser. We conclude the thesis by comparing the framework with other approaches